0  1  c7  c8
,
      etc.

We always exclude trivial solutions to (REF ) having all \(\alpha _J = 0\) . The singularities encoded in the Landau equations (REF ) and (REF ) are sometimes called first-type singularities, in contrast to second-type singularities which arise from pinch singularities at infinite loop momentum [1]}, [2]}, [3]}. The latter commonly arise from triangle subdiagrams; see for example the discussion in Sec. V of [4]}. Henceforth whenever we talk about Landau singularities, we only mean first-type singularities.
